Universal Distributed Feature Extraction Complementary to Side Information via H-Score

Abstract

This paper considers a distributed estimation system where edge nodes transmit averaged features to a center node for parameter estimation. A key challenge arises when the center node possesses auxiliary side information: how to design local extractors that are universally optimal for any downstream task, while avoiding redundancy with the side information. To tackle this problem, we orthogonally decompose the joint function space and demonstrate in the weak-dependence regime that the modal decomposition of the canonical dependence kernel's conditional-additive component yields optimal, task-independent features. We construct a distributed nested H-score to learn this decomposition and show that, under a limited feature budget, the mean-squared error (MSE) gap to the best task-specific features is determined solely by the task's alignment with the discarded, least informative modes, and vanishes to leading order for every square-integrable task once the budget is sufficient.

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BibTeX RIS

BibTeX

@misc{xinjie2026universal,
  title = {{Universal Distributed Feature Extraction Complementary to Side Information via H-Score}},
  author = {Yuan Xinjie and Dier Tang and Shao-Lun Huang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.16707},
  eprint = {2610.16707},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.16707},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Universal Distributed Feature Extraction Complementary to Side Information via H-Score
AU  - Yuan Xinjie
AU  - Dier Tang
AU  - Shao-Lun Huang
PY  - 2026
DA  - 2026/10/18
PB  - arXiv
DO  - 10.48550/arxiv.2610.16707
UR  - https://arxiv.org/abs/2610.16707
AB  - This paper considers a distributed estimation system where edge nodes transmit averaged features to a center node for parameter estimation. A key challenge arises when the center node possesses auxiliary side information: how to design local extractors that are universally optimal for any downstream task, while avoiding redundancy with the side information. To tackle this problem, we orthogonally decompose the joint function space and demonstrate in the weak-dependence regime that the modal decomposition of the canonical dependence kernel's conditional-additive component yields optimal, task-independent features. We construct a distributed nested H-score to learn this decomposition and show that, under a limited feature budget, the mean-squared error (MSE) gap to the best task-specific features is determined solely by the task's alignment with the discarded, least informative modes, and vanishes to leading order for every square-integrable task once the budget is sufficient.
ER  -

Abstract

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